CN102854505A - Weighting sparse-driven self-focusing SAR (Synthetic Aperture Radar) imaging method - Google Patents

Abstract

The invention discloses a weighting sparse-driven self-focusing SAR (Synthetic Aperture Radar) imaging method. The method comprises the steps as follows: establishing a linear observing model of echo data and an observing scene to construct the optimized target function; adopting the weighted L1 norm; and then carrying out an L1 norm approximating method to approximate the L1 norm in the target function; iterating and solving the optimized target function; and estimating the phase error of the linear observing model, and modifying the linear observing model to obtain a more accurate observing model, thus achieving the focusing of the synthetic aperture radar (SAR) image. Compared with the synthetic aperture radar (SAR) image reconstructed via a traditional focusing method (such as PGA (Programmable Gain Amplifier) and a sparse-driven auto-focusing (SDA), the synthetic aperture radar image obtained via the method provided by the invention is lower in sidelobe, and has a better effect on focusing.

Description

The sparse driving self-focusing of a kind of weighting SAR formation method

Technical field

The invention belongs to the radar imagery technical field, it has been particularly related to the synthetic aperture radar (SAR) technical field of imaging.

Background technology

Synthetic aperture radar (SAR) is a kind of high-resolution microwave imaging system, and the relative motion between its dependence radar and the target forms integrated array and obtains horizontal high resolving power, utilizes large bandwidth signal to realize vertical high resolving power.The synthetic aperture radar (SAR) imaging depends on the observation model of observation process, because the model error that kinematic error is introduced can cause echo data to have certain phase error, and then make reconstruct gained image defocus.The quality of reconstruct will be had a strong impact on after the image defocus, false target and high secondary lobe will be occurred.Produced auto-focus method in order to solve the image defocus problem.More famous a kind of auto-focus method is phase gradient self-focusing (PGA) method (seeing list of references " D.E.Wahl; P.H.Eichel, D.C.Ghiglia, and C.V.Jakowatz; Jr.; ' Phase Gradient Autofocus – A robust tool for high resolution SAR phase correction, ' IEEE Trans.Aerosp.Electron.Syst., Vol.30; No.7; 827 – 835,1994. " for details) at present, is a kind of traditional auto-focus method.

Sparse driving self-focusing (SDA) be a kind of auto-focus method of occurring in recent years (see for details list of references " Onhon N.Ozben,

M ü jdat. ' A Sparsity-driven Approach for Joint SAR Imaging and Phase Error Correction ' .IEEE Transactions on Image Processing, v 21, n 4, p 2075-2088, April 2012 ").Sparse driving self-focusing (SDA) adopts optimization method to solve phase error estimation and phase error and Image Reconstruction.Sparse driving self-focusing (SDA) is a kind of iterative method, at first obtain the estimated value of the scattering coefficient of a target scene according to the constraint condition of observation model and optimization problem, then obtain the phase error of observation model according to this estimated value, then according to this phase error corrections observation model, again the scattering coefficient of target scene is estimated, move in circles, until the difference of the estimated value of the scattering coefficient of current goal scene and estimated value last time stops circulation after less than default thresholding.In the sparse situation of scene, sparse driving self-focusing (SDA) method can better be reconstructed by Technologies Against Synthetic Aperture Radar (SAR) image, will be well than traditional auto-focus method (as: phase gradient self-focusing (PGA) method) focusing effect and secondary lobe lower, and sparse driving self-focusing (SDA) can obtain to have the full resolution pricture of Enhanced feature.Since sparse driving self-focusing (SDA) is adopted be the L1 norm constraint with and adopt the approximate mode of L1 norm accurate not, under the certain condition of data volume, it can better not carry out Image Reconstruction to the target scene, and the focusing effect of the image of its acquisition and Sidelobe Suppression effect can also further improve in the case.

Summary of the invention

The objective of the invention is for the focusing effect that further improves synthetic aperture radar (SAR) image under the condition of sparse scene and the secondary lobe that reduces the synthetic aperture radar (SAR) image.The present invention proposes the sparse driving self-focusing of a kind of weighting SAR formation method, the focus method (such as PGA) that the synthetic aperture radar (SAR) image ratio that adopts the inventive method to obtain the is traditional and synthetic aperture radar (SAR) image secondary lobe of sparse driving self-focusing (SDA) method reconstruct gained is lower, focusing effect is better.

Content of the present invention for convenience of description, at first do following term definition:

Definition 1, sparse driving self-focusing (SDA) method

Sparse driving auto-focus method is under the condition of sparse scene, model is echo data and the linear model of observing scene ideally, thereby obtain the linear measurement matrix, construct again optimization objective function, L1 norm in the objective function is carried out smooth approximate, then use method of steepest descent to find the solution this optimization objective function, according to the solution vector estimating phase error that obtains, and with this phase error corrections linear measurement matrix, to again find the solution optimization objective function in this revised linear measurement matrix substitution optimization objective function again, repeat said process, until the error between the solution vector that adjacent twice iterative obtains stops circulation less than predefined error threshold time side.Method detailed can referring to list of references " Onhon N.Ozben,

M ü jdat. ' A Sparsity-driven Approach for Joint SAR Imaging and Phase Error Correction ' .IEEE Transactions on Image Processing, v 21, and n 4, p2075-2088, April 2012.”

Definition 2, positive side-looking band pattern synthetic-aperture radar

Positive side-looking band pattern synthetic-aperture radar is that single array element is fixed on the motion platform, utilizes platform flying speed synthesizing one-dimensional array, can carry out to surveying and drawing the zone a kind of polarization sensitive synthetic aperture radar system of two-dimensional imaging.

Definition 3, positive side-looking band pattern synthetic-aperture radar theoretical resolution

Positive side-looking band pattern synthetic-aperture radar theoretical resolution refers to according to positive side-looking band pattern polarization sensitive synthetic aperture radar system parameter, comprise transmitted signal bandwidth, the ultimate resolution that the positive side-looking band pattern synthetic-aperture radar that length of synthetic aperture and antenna length determine can reach comprises azimuth dimension resolution and distance dimension resolution.

Definition 4, positive side-looking band pattern synthetic-aperture radar observation scene

Positive side-looking band pattern synthetic-aperture radar observation scene refers to the set of all scene objects points to be observed in the realistic space, is a two-dimensional ribbon there parallel with positive side-looking band pattern synthetic-aperture radar movement locus.Different expressions is arranged, in case but later on its expression of coordinate system establishment is unique under the different spaces coordinate system.Generally speaking in order to make things convenient for imaging to get earth axes.

Definition 5, positive side-looking band pattern data of synthetic aperture radar space

Positive side-looking band pattern data of synthetic aperture radar space is the echoed signal space that side-looking band pattern synthetic-aperture radar echo data consists of of making a comment or criticism.

Definition 6, positive side-looking band pattern synthetic aperture radar image-forming space

Positive side-looking band pattern synthetic aperture radar image-forming space refers to use formation method by the image space of the resulting two-dimentional synthetic-aperture radar in positive side-looking band pattern data of synthetic aperture radar space.

Definition 7, positive side-looking band pattern synthetic aperture radar image-forming scene reference point

Positive side-looking band pattern synthetic-aperture radar scene reference point is certain scattering point in the side-looking band pattern synthetic aperture radar image-forming space of making a comment or criticism, as the reference of analyzing and process other scattering points in the scene.

Definition 8, flight aperture

The flight aperture refers to jointly shine from the transmitting-receiving wave beam for the scattering point of mapping in the scene and begins to launching beam or any one irradiation of received beam less than the distance that finishes the transmitting-receiving beam center and pass by.

Definition 9, slow time and fast time

The slow time refers to that transmit-receive platform flies over a flight needed time of aperture, because radar is with certain repetition period T _rLaunch received pulse, can be expressed as the time variable t of a discretize at slow constantly n _s(n)=nT _r, n=1,2 ..., N _a, N _aBe expressed as the discrete number of slow time in the synthetic aperture.

The fast time refers to the time of the one-period of radar emission received pulse, is with sample rate f because radar receives echo _sSample, can be expressed as the time variable of a discretize at fast constantly m M=1,2 ..., N _r, N _rBe expressed as a repetition period T _rThe discrete number of interior fast time.

Definition 10, time delay

Be that transmitter transmits signals to receiver and receives this section of signal period time delay, is designated as τ, and it determines by the distance R of observation area to this system,

Wherein, C is the light velocity.

Definition 11, synthetic-aperture radar transmitter

The synthetic-aperture radar transmitter refers to the system to the observation area transmission of electromagnetic signals that present synthetic-aperture radar adopts, and mainly comprises the modules such as signal generator, frequency mixer, amplifier.

Definition 12, synthetic-aperture radar receiver

The synthetic-aperture radar receiver refers to the system of the reception observation area echo that present synthetic-aperture radar adopts, and mainly comprises frequency mixer, amplifier, A/D converter, memory device etc.

Definition 13, Matlab

Matlab is the abbreviation of matrix experiment chamber (Matrix Laboratory), the business mathematics software that U.S. MathWorks company produces is for advanced techniques computational language and the interactive environment of algorithm development, data visualization, data analysis and numerical evaluation.Detailed directions sees document " MATLAB 5 handbooks " for details, and EvaPart-Enander etc. write, and China Machine Press publishes.

Definition 14, norm

If X is number field C Linear Space, claim || || be the norm on the X (norm), if it satisfies: 1. orthotropicity: || X|| 〉=0, and || X||=0＜=＞X=0; 2. homogeneous property: || α X||=|a|||X||; 3. subadditivity (triangle inequality): || X+Y||≤|| X||+||Y||.If

Be N ₀* 1 dimension discrete signal, vectorial X LP norm is The L1 norm is

The L2 norm is

N wherein ₀Be positive integer, () ^TBe matrix transpose.

Definition 15, rectangular function and exponential function

If x is the number on the number field R, then

If x is the plural exp (x)=e on the complex field C ^x, wherein e is the truth of a matter of natural logarithm.

Definition 16, matrix transpose and conjugate transpose

If matrix

Wherein C is complex field, N ₀With M ₀Be positive integer, note A ^TFor the transposition of matrix A, with () ^TNote is done matrix transpose, and the transposition of matrix A is got the associate matrix A that conjugation can obtain matrix A ^H, with () ^HNote is done conjugate transpose.

Definition 17, diag () and ln ()

The expression diagonal element is

M ₀* M ₀The dimension square formation, wherein

Be the number on the number field C, M ₀Be positive integer.

Ln () is defined as natural logarithm.

Definition 18, Re{} and Im{}

Suppose that x is the number of complex field C, x can be expressed as Re{x}+jIm{x}, wherein j is pure imaginary number, and Re{x} is the real part of x, and Im{x} is the imaginary part of x.

Definition 19, sparse signal and sparse scene

If the number of nonzero value is much smaller than the length of signal itself in discrete signal, then this signal can be thought sparse.If

Be 1 * N ₀The column vector that the dimension discrete signal forms, () ^TBe transpose operator number.If K is only arranged among the vectorial X ₀(K ₀Much smaller than N ₀) individual nonzero element or much larger than the number of zero element, then X is K ₀Sparse vector,

Be the degree of rarefication of signal X, K ₀Be positive integer, N ₀Be positive integer.If when the number of a scene moderately and strongly inverse scattering point is very little with respect to the scene size, can think that then this scene is sparse scene.

The invention provides the sparse driving self-focusing of a kind of weighting synthetic aperture radar image-forming method, it comprises following step, as shown in Figure 2:

The parameter of step 1, the positive side-looking band pattern of initialization polarization sensitive synthetic aperture radar system parameter and the sparse driving auto-focus method of weighting:

Be initialized to as systematic parameter and comprise: the light velocity, note is C; The platform speed vector, note is done

Platform initial position vector, note is done

The platform initial position is to the bee-line of observation band, and note is R ₀The electromagnetic wave number of radar emission, note is K ₀The signal bandwidth of radar emission baseband signal, note is B; The radar emission signal pulse width, note is T _PThe radar received beam continues width, and note is T _oThe sample frequency of Radar Receiver System, note is f _sThe pulse repetition rate of radar system, note is PRF; Radar Receiver System receives the ripple door with respect to the delay of the transmitted wave door that transmits, and note is T _DThe length of synthetic aperture of radar, note is L _SarThe observation scope of two-dimensional observation scene distance dimension, note is [r _Min, r _Max], r wherein _MinBe the lower limit of two-dimensional observation scene distance dimension observation scope, r _MaxThe upper limit for two-dimensional observation scene distance dimension observation scope; The observation scope of two-dimensional observation scene azimuth dimension, note is [α _Min, a _Max], a wherein _MinBe the lower limit of two-dimensional observation scene azimuth dimension observation scope, a _MaxThe upper limit for two-dimensional observation scene azimuth dimension observation scope; Synthetic-aperture radar is apart from dimension resolution, and note is Δ r; Synthetic-aperture radar azimuth dimension resolution, note is Δ x; The azimuth dimension sampling number, note is N ₁Distance dimension sampling number, note is N ₂Above-mentioned parameter is the canonical parameter of positive side-looking band pattern polarization sensitive synthetic aperture radar system, and wherein, the platform initial position is to the distance R of scene reference point _c, the electromagnetic wave number K of radar emission ₀, the signal bandwidth B of radar emission baseband signal, radar emission signal pulse width T _P, the radar received beam continues width T _o, the sample frequency f of Radar Receiver System _s, the pulse repetition rate PRF of radar system, Radar Receiver System receive the ripple door with respect to the delay T of the transmitted wave door that transmits _D, the length of synthetic aperture L of radar _Sar, synthetic-aperture radar is apart from dimension resolution ax/r, synthetic-aperture radar azimuth dimension resolution ax/x, azimuth dimension sampling number N ₁Distance dimension sampling number N ₂, in positive side-looking band pattern synthetic-aperture radar design process, determine; Wherein, platform speed vector

Platform initial position vector

Observation scope [a of two-dimensional observation scene azimuth dimension _Min, a _Max] and the observation scope [r of two-dimensional observation scene distance dimension _Min, r _Max] in positive side-looking band pattern synthetic-aperture radar observation program design, determine; According to existing positive side-looking band pattern polarization sensitive synthetic aperture radar system and positive side-looking band pattern synthetic-aperture radar observation program, positive side-looking band pattern synthetic aperture radar image-forming method needs be initialized to be as systematic parameter known.The sparse driving auto-focus method of initialization weighting parameter comprises: Lagrangian coefficient, and note is λ; L1 norm Constant of Approximation, note is β; The sparse driving auto-focus method of weighting is found the solution error threshold, and note is ε; Maximum iteration time, note is MC.Above-mentioned parameter is the required parameter of the sparse driving auto-focus method of weighting, wherein, Lagrangian coefficient lambda, L1 norm Constant of Approximation β, the sparse driving auto-focus method of weighting is found the solution error threshold ε, maximum iteration time MC, being in advance provides.

Step 2, structure radar echo signal and the Systems with Linear Observation model of observing the scene scattering coefficient

May further comprise the steps:

Step 2.1:

Observation scope [r with two-dimensional observation scene distance dimension _Min, r _Max] be divided into N distance dimension unit so that distance dimension resolution ax/r is equally spaced as the interval, note do distance dimension unit 1, distance tie up unit 2 ..., distance dimension unit N, wherein N is positive integer.In like manner, with the observation scope [α of two-dimensional observation scene azimuth dimension _Min, α _Max] uniformly-spaced being divided into M azimuth dimension unit as the interval take azimuth dimension resolution ax/x, note is done azimuth dimension unit 1, and the position vector note of azimuth dimension unit 1 is done Azimuth dimension unit 2, the position vector note of azimuth dimension unit 2 is done

, azimuth dimension unit M, the position vector of azimuth dimension unit M note is done

Wherein M is positive integer.Through after the above-mentioned processing, as shown in Figure 3, the two-dimensional observation scene is divided into K cell, observation scene cell number K=NM, comprise M azimuth dimension unit and N distance dimension unit in K the cell, i azimuth dimension unit in M azimuth dimension unit and N distance are tieed up in the unit l and are remembered apart from the position vector of tieing up the determined cell in unit and do

I=1,2 ..., M, l=1,2 ..., N.The scattering coefficient of two-dimensional observation scene is expressed as vectorial α=[α ₁..., α _i..., α _M] ^T, α wherein _iBe i the subvector of α, α _i=[α _{I, 1}..., α _{I, l}..., α _{I, N}] be the scattering coefficient vector of azimuth dimension unit i, α ₁α during for i=1 _iValue, α _Mα during for i=M _iValue, α _{I, l}Be α _iL element, α _{I, l}The expression cell

Electromagnetic scattering coefficient, α _{I, 1}α during for l=1 _{I, l}Value, α _{I, N}α during for l=N _{I, l}Value, i=1,2 ..., M, l=1,2 ..., N, () _TBe matrix transpose.

Step 2.2:

Synthetic-aperture radar echo data vector note is done

Wherein () ^TBe matrix transpose,

Be the echo data vector that slow constantly n receives, y ₁Y during for n=1 _nValue,

Be n=N ₁The time y _nValue, y _{N, m}For synthetic-aperture radar at slow constantly n, the echo data that fast constantly m receives, y _{N, 1}Y during for m=1 _{N, m}Value,

Be m=N ₂The time y _{N, m}Value, slow constantly n=1,2 ..., N1, fast constantly m=1,2 ..., N ₂, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number.

Step 2.3:

Structure linear measurement matrix is

Wherein () ^TBe matrix transpose,

Be n the submatrix of Φ,

During for n=1

Value,

Be n=N ₁The time

Value, slow constantly n=1,2 ..., N ₁, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number, φ _{N, m}For

M subvector, φ _{N, m}=[γ _{N, m}(1,1), γ _{N, m}(1,2) ..., γ _{N, m}(i, l) ..., γ _{N, m}(M, N-1), γ _{N, m}(M, N)] ^T, φ _{N, 1}φ during for m=1 _{N, m}Value,

Be m=N ₂The time φ _{N, m}Value, fast constantly m=1,2 ..., N ₂, N ₂Be distance dimension sampling number, ${\mathrm{\γ}}_{n,m}(i,l)=\mathrm{rect}\left(\frac{2{\left|\right|{\stackrel{\‾}{x}}_i-{\stackrel{\‾}{P}}_n\left|\right|}_2}{L_{\mathrm{sar}}}\right)\·\mathrm{rect}\left(\frac{t_f\left(m\right)-\mathrm{\τ}}{T_p}\right)\·\exp \left(\mathrm{j\π}{K}_r{(t_f\left(m\right)-\mathrm{\τ})}^2\right),$ γ _{N, m}γ when (1,1) is i=1 and l=1 _{N, m}(i, l) value, γ _{N, m}(1,2 γ when being i=1 and l=2 _{N, m}(i, l) value, γ _{N, m}(M, γ when N-1 is i=M and l=N-1 _{N, m}(i, l) value, γ _{N, m}γ when (M, N) is i=M and l=N _{N, m}(i, l) value, j is pure imaginary number, i=1,2 ..., M, l=1,2 ..., N,

Be the position vector of i azimuth dimension unit of two-dimensional observation scene, L _SarBe the length of synthetic aperture of radar, t _f(m) be the fast constantly time variable of m, chirp rate

B is the signal bandwidth of radar emission baseband signal, T _PBe the radar emission signal pulse width,

|| || ₂Be the L2 norm, C is the light velocity, the slow constantly position vector of n platform

Be the platform speed vector,

Be platform initial position vector, PRF is the pulse repetition rate of radar system, For in the two-dimensional observation scene that obtains in the step 2.1 by the position vector of azimuth dimension unit i with the determined cell of distance dimension unit l, slow constantly n=1,2 ..., N ₁, fast constantly m=1,2 ..., N ₂, i=1,2 ..., M, l=1,2 ..., N, M is observation scene azimuth dimension unit number, N is observation scene distance dimension unit number, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number.

Step 2.4:

From 1 to N ₂This N ₂Randomly draw Num in the individual positive integer ₀Individual positive integer and to this Num ₀Individual positive integer obtains the 1st group of positive integer by sorting from small to large, the 1st positive integer note of the 1st group of positive integer done

The 2nd positive integer note of the 1st group of positive integer done

, the Num of the 1st group of positive integer ₀Individual positive integer note is done

In like manner, from 1 to N ₂This N ₂Randomly draw Num in the individual positive integer ₀Individual positive integer and to this Num ₀Individual positive integer obtains the 2nd group of positive integer by sorting from small to large, the 1st positive integer note of the 2nd group of positive integer done

The 2nd positive integer note of the 2nd group of positive integer done , the Num of the 2nd group of positive integer ₀Individual positive integer note is done

, by that analogy, from 1 to N ₂This N ₂Randomly draw Num in the individual positive integer ₀Individual positive integer and to this Num ₀Individual positive integer obtains N by sorting from small to large ₁The group positive integer, N ₁The 1st positive integer note of group positive integer done

N ₁The 2nd positive integer note of group positive integer done

, N ₁The Num of group positive integer ₀Individual positive integer note is done

Num wherein ₀For being less than or equal to N ₂Positive integer, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number.With the echo data vector that obtains in the step 2.2

In the echo data vector that receives of slow constantly n

In

Column element

The

Column element

, the

Column element

Composition of vector

Slow constantly n=1,2 ..., N ₁, obtain thus N ₁Individual vector

During for n=1 Value,

Be n=N ₁The time Value is with the N that obtains ₁Individual vector

Form the echo data vector

Wherein () ^TBe matrix transpose, For

N subvector, slow constantly n=1,2 ..., N ₁, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number.With the linear measurement matrix that obtains in the step 2.3

In n submatrix In Column element

The

Column element

, the

Column element

Form matrix

Slow constantly n=1,2 ..., N ₁, obtain thus N ₁Individual matrix

During for n=1

Value,

Be n=N ₁The time

Value is with the N that obtains ₁Individual matrix

Form the linear measurement matrix

Wherein () ^TBe matrix transpose,

For

N submatrix, slow constantly n=1,2 ..., N ₁, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number.The Systems with Linear Observation model of definition observation scene scattering coefficient and radar return data is expressed as

Wherein

For with The Gaussian noise vector that dimension is identical, α is observation scene scattering coefficient vector.

The cost function of step 3, the sparse auto-focus method of structure weighting

The cost function of the sparse auto-focus method of structure weighting is

F=[f wherein ₁..., f _k..., f _K] ^TBe solution vector, f _kBe k element of solution vector, f ₁F during for k=1 _kValue,, f _KF during for k=K _kValue, k=1,2 ..., K, K is the number of observation scene cell, λ is Lagrangian coefficient,

The echo data vector that obtains for step 2.4,

The linear measurement matrix that obtains for step 2.4, || || ₁Be the L1 norm, || || ₂Be L2 norm, () ^TBe matrix transpose, the definition weighting matrix $W_1=\mathrm{diag}(\frac{1}{\left|f_1\right|+\mathrm{\β}},\·\·\·,\frac{1}{\left|f_k\right|+\mathrm{\β}},\·\·\·,\frac{1}{\left|f_K\right|+\mathrm{\β}}),$ The L1 norm approximate value of getting solution vector f is ${\left|\right|f\left|\right|}_1\≈\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\left(\right|f_k|-\mathrm{\β}\·\ln (\mathrm{\β}+|f_k\left|\right)),$ β is L1 norm Constant of Approximation.

The image-forming step of step 4, the sparse auto-focus method of weighting

May further comprise the steps:

Step 4.1:

The linear measurement matrix that defines the 0th iteration acquisition is

Order The linear measurement matrix that equals to obtain in the step 2.4 Wherein

Be Φ ⁽⁰⁾N submatrix,

During for n=1

Value,

Be n=N ₁The time

Value, slow constantly n=1,2 ..., N ₁, N ₁Be azimuth dimension sampling number, () ^TBe matrix transpose.The solution vector that defines the 0th iteration acquisition is

Wherein

Be f ⁽⁰⁾K element,

During for k=1 Value,

During for k=K

Value, k=1,2 ..., K, K is the number of observation scene cell, order

Wherein

Be the echo data vector that obtains in the step 2.4, () ^HBe conjugate transpose.Definition count is the iterations counting variable, count=1, and 2 ..., MC.Definition cc is iteration number of times of iteration when stopping, and cc is positive integer.Forward step 4.2.1 to, carry out iteration the 1st time.

Step 4.2.1:

Carry out iteration the 1st time, iterations counting variable count=1, the step of the 1st iteration comprises step 4.3.1,4.4.1,4.5.1,4.6.1,4.7.1.Forward step 4.3.1 to.

Step 4.3.1:

Definition $W^{\left(1\right)}=\mathrm{diag}(\frac{1}{{\left(\right|f_1^{\left(0\right)}|+\mathrm{\β})}^2},\·\·\·,\frac{1}{{\left(\right|f_k^{\left(0\right)}|+\mathrm{\β})}^2},\·\·\·,\frac{1}{{\left(\right|f_K^{\left(0\right)}|+\mathrm{\β})}^2})$ Be the weighting matrix of the 1st iteration, wherein

Be the solution vector that the 0th time iteration obtains,

Be f ⁽⁰⁾K element,

During for k=1

Value, During for k=K

Value, k=1,2 ..., K, K is the number of observation scene cell, β is L1 norm Constant of Approximation, () ^TBe matrix transpose.Forward step 4.4.1 to.

Step 4.4.1:

Definition

Be the solution vector of the 1st iteration acquisition, wherein

Be f ⁽¹⁾K element,

During for k=1

Value,

During for k=K

Value, k=1,2 ..., K, K is the number of observation scene cell, () ^TBe matrix transpose.Order Wherein

Be the linear measurement matrix that the 0th iteration obtains, W ⁽¹⁾Be the weighting matrix that the 1st time iteration obtains,

Be the echo data vector that obtains in the step 2.4, λ is Lagrangian coefficient, () ^HBe conjugate transpose.Forward step 4.5.1 to.

Step 4.5.1:

Definition Be the 1st the slow constantly phase error of n of iteration, wherein

() ^HBe conjugate transpose,

It is the linear measurement matrix that the 0th iteration obtains

N submatrix,

The echo data vector that obtains for step 2.4 N subvector, slow constantly n=1,2 ..., N ₁, f ⁽¹⁾Be the solution vector that the 1st time iteration obtains, arctan () is arctan function, N ₁Be the azimuth dimension sampling number.Forward step 4.6.1 to.

Step 4.6.1:

Definition

Be the linear measurement matrix of the 1st iteration, wherein

For

N submatrix,

It is the linear measurement matrix that the 0th iteration obtains

N submatrix,

During for n=1

Value,

Be n=N ₁The time Value, slow constantly n=1,2 ..., N ₁, j is pure imaginary number, () ^TBe matrix transpose,

Be the 1st the slow constantly phase error of n of iteration, N ₁Be the azimuth dimension sampling number.Forward step 4.7.1 to.

Step 4.7.1:

If

Value less than ε or count equals maximum iteration time MC, then, makes cc=1, and iteration stops, and forwards step 4.3 to; Otherwise, carry out iteration the 2nd time, forward step 4.2.2 to, wherein cc is iteration number of times of iteration when stopping, ε is error threshold, f ⁽⁰⁾Be the solution vector that the 0th time iteration obtains, f ⁽¹⁾Be the solution vector that the 1st time iteration obtains, MC is maximum iteration time, || || ₂Be the L2 norm.

Step 4.2.2:

Carry out iteration the 2nd time, count=2, the 2nd time iterative step comprises step 4.3.2,4.4.2,4.5.2,4.6.2,4.7.2.Forward step 4.3.2 to.

Step 4.3.2:

Definition $W^{\left(2\right)}=\mathrm{diag}(\frac{1}{{\left(\right|f_1^{\left(1\right)}|+\mathrm{\β})}^2},\·\·\·,\frac{1}{{\left(\right|f_k^{\left(1\right)}|+\mathrm{\β})}^2},\·\·\·,\frac{1}{{\left(\right|f_K^{\left(1\right)}|+\mathrm{\β})}^2})$ Be the weighting matrix of the 2nd iteration, wherein

Be the solution vector that the 1st time iteration obtains,

Be f ⁽¹⁾K element, During for k=1

Value,

During for k=K

Value, k=1,2 ..., K, K is the number of observation scene cell, β is L1 norm Constant of Approximation, () ^TBe matrix transpose.Forward step 4.4.2 to.

Step 4.4.2:

Definition

Be the solution vector of the 2nd iteration acquisition, wherein

Be f ⁽²⁾K element,

During for k=1

Value, During for k=K

Value, k=1,2 ..., K, K is the number of observation scene cell, () ^TBe matrix transpose.Order

Wherein

Be the linear measurement matrix that the 1st iteration obtains, W ⁽²⁾Be the weighting matrix that the 2nd time iteration obtains,

Be the echo data vector that obtains in the step 2.4, λ is Lagrangian coefficient, () ^HBe conjugate transpose.Forward step 4.5.2 to.

Step 4.5.2:

Definition

Be the 2nd the slow constantly phase error of n of iteration, wherein

() ^HBe conjugate transpose, It is the linear measurement matrix that the 1st iteration obtains

N submatrix,

The echo data vector that obtains for step 2.4

N subvector, slow constantly n=1,2 ..., N ₁, f ⁽²⁾Be the solution vector that the 2nd time iteration obtains, arctan () is arctan function, N ₁Be the azimuth dimension sampling number.Forward step 4.6.2 to.

Step 4.6.2:

Definition

Be the linear measurement matrix of the 2nd iteration, wherein

For

N submatrix,

It is the linear measurement matrix that the 1st iteration obtains

N submatrix,

During for n=1 Value,

Be n=N ₁The time

Value, slow constantly n=1,2 ..., N ₁, j is pure imaginary number, () ^TBe matrix transpose,

Be the 2nd the slow constantly phase error of n of iteration, N ₁Be the azimuth dimension sampling number.Forward step 4.7.2 to.

Step 4.7.2:

If

Value less than ε or count equals maximum iteration time MC, then, makes cc=2, and iteration stops, and forwards step 4.3 to; Otherwise, carry out iteration the 3rd time, forward step 4.2.3 to, wherein cc is iteration number of times of iteration when stopping, ε is error threshold, f ⁽¹⁾Be the solution vector that the 1st time iteration obtains, f ⁽²⁾Be the solution vector that the 2nd time iteration obtains, MC is maximum iteration time, || || ₂Be the L2 norm.

Step: 4.2.3

In like manner, by that analogy, carry out the 3rd iteration ..., the MC-1 time iteration.

The MC time iteration of step 4.2.:

Carry out iteration the MC time, count=MC,

This moment, the value of iterations count equaled MC, made cc=MC, and termination of iterations forwards step 4.3 to;

Step 4.3:

The solution vector f that obtains according to the cc time iteration ^(cc), obtain the observation scene scattering coefficient vector α=f that constructs in the step 2.1 ^(cc), cc is iteration number of times of iteration when stopping.By observation scene scattering coefficient vector α=[α ₁..., α _i..., α _M] ^T, i the subvector of α is α _i=[α _{I, 1}..., α _{I, l}..., α _{I, N}], α ₁α during for i=1 _iValue, α _Mα during for i=M _iValue, α _{I, l}Be α _iL element, α _{I, 1}α during for l=1 _{I, l}Value, α _{I, N}α during for l=N _{I, l}Value, i=1,2 ..., M, l=1,2 ..., N obtains the final imaging results of synthetic-aperture radar two-dimensional scene A wherein _i=[α _{I, 1}..., α _{I, l}..., α _{I, N}], A ₁A during for i=1 _iValue, A _MA during for i=M _iValue, () ^TBe matrix transpose, i=1,2 ..., M, l=1,2 ..., N, M are the unit number of azimuth dimension, N is the number of distance dimension unit.

Through above-mentioned steps, namely obtain the positive side-looking band pattern diameter radar image based on the sparse auto-focus method of weighting.

Innovative point of the present invention: be to have proposed the sparse self-focusing of weighting (WSDA) method, the method is improved the optimization objective function in sparse driving self-focusing (SDA) method, L1 norm constraint wherein is revised as weighting L1 norm constraint, and uses another L1 norm approximation method.The synthetic aperture radar (SAR) image secondary lobe that the focus method (such as PGA) that the obtainable synthetic aperture radar (SAR) image ratio of the method is traditional and the reconstruct of sparse driving self-focusing (SDA) method obtain is lower, focusing effect is better.

Ultimate principle of the present invention: set up echo data and the Systems with Linear Observation model of observing scene, the structure optimization objective function, use the L1 norm of weighting, then use the approximate mode of a kind of L1 norm that L1 norm in the objective function is similar to, then iterative optimization objective function, estimate the phase error of Systems with Linear Observation model and the Systems with Linear Observation model revised to obtain a more accurately observation model, thereby realize the focusing of synthetic aperture radar (SAR) image.

Advantage of the present invention: for sparse scene, the sparse self-focusing of weighting (WSDA) method can better the Technologies Against Synthetic Aperture Radar observation model phase error estimate, thereby obtain more accurately Systems with Linear Observation model, and the method can obtain more sparse solution, thereby the secondary lobe of the synthetic aperture radar (SAR) image that (such as PGA etc.) and sparse driving self-focusing (SDA) method obtain so that the traditional auto-focus method of the synthetic aperture radar (SAR) image ratio that the method obtains is lower, focusing effect is better.

Description of drawings

Fig. 1 is positive side-looking band pattern synthetic-aperture radar geometry figure

Wherein,

Velocity for aircraft; X, Y, Z are three-dimensional system of coordinate; O is zero point of reference frame.

Fig. 2 is method flow diagram of the present invention

Fig. 3 is synthetic-aperture radar two-dimensional observation scene unit lattice dividing mode

Wherein, M is azimuth dimension unit number; N is distance dimension unit number.

Fig. 4 is the parameter list of the sparse driving auto-focus method of weighting

Fig. 5 is synthetic aperture radar image-forming system emulation parameter list

Embodiment

The present invention mainly adopts the mode of emulation experiment to verify the feasibility of this system model, and institute in steps, conclusion is all correct in MATLAB7.9.0 checking.The implementation step is as follows:

The setting of the parameter of step 1, radar system parameter and the sparse driving auto-focus method of weighting

The systematic parameter that this step embodiment adopts sees Fig. 5 for details, and the parameter that the sparse driving auto-focus method of weighting adopts sees Fig. 4 for details.

Step 2, structure radar echo signal and the Systems with Linear Observation model of observing the scene scattering coefficient

May further comprise the steps:

Step 2.1:

The observation scope [22.5 meters, 22.5 meters] of two-dimensional observation scene distance dimension is divided into 61 distance dimension unit so that 0.75 meter of distance dimension resolution is equally spaced as the interval, note do distance dimension unit 1, distance dimension unit 2 ..., distance dimension unit 61.In like manner, the observation scope [9 meters, 9 meters] of two-dimensional observation scene azimuth dimension uniformly-spaced is divided into 61 azimuth dimension unit take 0.3 meter of azimuth dimension resolution as the interval, note is done azimuth dimension unit 1, and the position vector note of azimuth dimension unit 1 is done

Azimuth dimension unit 2, the position vector note of azimuth dimension unit 2 is done , azimuth dimension unit 61, the position vector of azimuth dimension unit 61 note is done

Through after the above-mentioned processing, as shown in Figure 3, the two-dimensional observation scene is divided into K cell, observation scene cell number K=3721, comprise 61 azimuth dimension unit and 61 distance dimension unit in 3721 cells, in i azimuth dimension unit in 61 azimuth dimension unit and 61 the distance dimension unit l remembers apart from the position vectors of tieing up the determined cell in unit and does

I=1,2 ..., 61, l=1,2 ..., 61.The scattering coefficient of two-dimensional observation scene is expressed as vectorial α=[α ₁..., α _i..., α ₆₁] ^T, α wherein _i=[α _{I, 1}..., α _{I, l}..., α _{I, 61}] be the scattering coefficient vector of azimuth dimension unit i, α _{I, l}The expression cell

Electromagnetic scattering coefficient, i=1,2 ..., 61, l=1,2 ..., 61, () ^TBe matrix transpose.

Step 2.2:

Synthetic-aperture radar echo data vector note is y=[y ₁..., y _n..., y ₁₂₈] ^T, wherein () ^TBe matrix transpose, y _n=[y _{N, 1}..., y _{N, m}..., y _{N, 128}] be the echo data vector that slow constantly n receives, y _{N, m}For synthetic-aperture radar at slow constantly n, the echo data that fast constantly m receives, slow constantly n=1,2 ..., 128, fast constantly m=1,2 ..., 128, the azimuth dimension sampling number is 128, distance dimension sampling number is 128.

Step 2.3:

Structure linear measurement matrix is

Wherein () ^TBe matrix transpose, Slow constantly n=1,2 ..., 12, the azimuth dimension sampling number is 128, φ _{N, m}=[γ _{N, m}(1,1), γ _{N, m}(1,2) ..., γ _{N, m}(i, l) ..., γ _{N, m}(61,60), γ _{N, m}(61,61)] ^T, () ^TBe matrix transpose, slow constantly n=1,2 ..., 1, fast constantly m=1,2 ..., 1, distance dimension sampling number is 128, ${\mathrm{\γ}}_{n,m}(i,l)=\mathrm{rect}\left(\frac{2{\left|\right|{\stackrel{\‾}{x}}_i-{\stackrel{\‾}{P}}_n\left|\right|}_2}{L_{\mathrm{sar}}}\right)\·\mathrm{rect}\left(\frac{t_f\left(m\right)-\mathrm{\τ}}{T_p}\right)\·\exp \left(\mathrm{j\π}{K}_r{(t_f\left(m\right)-\mathrm{\τ})}^2\right),$ J is pure imaginary number, i=1, and 2 ..., 61, l=1,2 ..., 61,

Be the position vector of i azimuth dimension unit of two-dimensional observation scene, the length of synthetic aperture L of radar _Sar=15 meters, t _f(m) be the fast constantly time variable of m, chirp rate K _r=3 * 10 ¹⁴, the signal bandwidth B=150 of radar emission baseband signal * 10 ⁶Megahertz, radar emission signal pulse width T _P=5 * 10 ^-7Second,

|| || ₂Be the L2 norm, light velocity C=3 * 10 ⁸, the slow constantly position vector of n platform

Be the platform speed vector,

Be platform initial position vector, the pulse repetition rate PRF=500 hertz of radar system,

For in the two-dimensional observation scene by the position vector of azimuth dimension unit i with the determined cell of distance dimension unit l, slow constantly n=1,2 ..., 128, fast constantly m=1,2 ..., 128, i=1,2 ..., 61, l=1,2 ..., 61.

Step 2.4:

Randomly draw 20 positive integers from 1 to 128 these 128 positive integers and these 20 positive integers are obtained the 1st group of positive integer by sorting from small to large, the 1st positive integer note of the 1st group of positive integer done

The 2nd positive integer note of the 1st group of positive integer done

, the 20th positive integer note of the 1st group of positive integer done

In like manner, randomly draw 20 positive integers from 1 to 128 these 128 positive integers and these 20 positive integers are obtained the 2nd group of positive integer by sorting from small to large, the 1st positive integer note of the 2nd group of positive integer done

The 2nd positive integer note of the 2nd group of positive integer done

, the 20th positive integer note of the 2nd group of positive integer done , the rest may be inferred, randomly draws 20 positive integers from 1 to 128 these 128 positive integers and these 20 positive integers are obtained the 128th group of positive integer by sorting from small to large, and the 1st positive integer note of the 128th group of positive integer done

The 2nd positive integer note of the 128th group of positive integer done

, the 20th positive integer note of the 128th group of positive integer done With the echo data vector y=[y that obtains in the step 2.2 ₁..., y _n..., y ₁₂₈] ^TIn the echo data vector y that receives of slow constantly n _n=[y _{N, 1}..., y _{N, m}... among the y

Column element

The

Column element

, the

Column element

Composition of vector

Slow constantly n=1,2 ..., 128, obtain thus 128 vectors

With 128 vectors that obtain Form the echo data vector

Wherein () ^TBe matrix transpose,

For

The 1st subvector, For

The 2nd subvector ..., For

The 128th subvector.With the linear measurement matrix that obtains in the step 2.3

In n submatrix

In Column element The

Column element

, the

Column element Form matrix

Slow constantly n=1,2 ..., 12, obtain thus 128 matrixes With 128 matrixes that obtain

Form the linear measurement matrix

Wherein () ^TBe matrix transpose,

For The 1st submatrix,

For

The 2nd submatrix ...,

For

The 128th submatrix.The Systems with Linear Observation model of structure observation scene scattering coefficient and radar return data is expressed as

Wherein

For with

The Gaussian noise vector that dimension is identical, α is observation scene scattering coefficient vector.

The cost function of step 3, the sparse auto-focus method of structure weighting

The cost function of the sparse auto-focus method of structure weighting is

F=[f wherein ₁..., f _k..., f ₃₇₂₁] ^TBe solution vector, f _kBe k element of solution vector, k=1,2 ..., 3721, Lagrangian coefficient lambda=40,

The echo data vector that obtains for step 2.4,

Be the linear measurement matrix that step 2.4 obtains, the definition weighting matrix $W_1=\mathrm{diag}(\frac{1}{\left|f_1\right|+\mathrm{\&beta;}},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{\left|{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002117515400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\right|+\mathrm{\&beta;}},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{\left|f_{3721}\right|+\mathrm{\&beta;}}),$ () ^TBe matrix transpose, the L1 norm approximate value of getting solution vector f is L1 norm Constant of Approximation β=10 ^-2, || || ₁Be the L1 norm, || || ₂Be the L2 norm.

The image-forming step of step 4, the sparse auto-focus method of weighting

May further comprise the steps:

Step 4.1:

The linear measurement matrix of the 0th iteration

The linear measurement matrix that equals to obtain in the step 2.4

Wherein

Be Φ ⁽⁰⁾N submatrix, slow constantly n=1,2 ..., 128, () ^TBe matrix transpose.The solution vector of the 0th iteration Wherein

Be the echo data vector that obtains in the step 2.4, () ^HBe conjugate transpose.Definition count iterations counting variable, count=1,2 ..., 100.Definition cc is iteration number of times of iteration when stopping, and cc is positive integer.Forward step 4.2.1 to, carry out iteration the 1st time.

Step 4.2.1:

Carry out iteration the 1st time, count=1 comprises step 4.3.1 ~ 4.7.1.Forward step 4.3.1 to.

Step 4.3.1:

Definition $W^{\left(1\right)}=\mathrm{diag}(\frac{1}{{\left(\right|f_1^{\left(0\right)}|+\mathrm{\&beta;})}^2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{\left(\right|f_k^{\left(0\right)}|+\mathrm{\&beta;})}^2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{\left(\right|f_{3721}^{\left(0\right)}|+\mathrm{\&beta;})}^2})$ Be the weighting matrix of the 1st iteration, wherein

Be the solution vector that the 0th time iteration obtains,

Be f ⁽⁰⁾K element,

During for k=1

Value,

During for k=3721

Value, k=1,2 ..., 37, β=10 ^-2Be L1 norm Constant of Approximation, () ^TBe matrix transpose.Forward step 4.4.1 to.

Step 4.4.1:

Definition

Be the solution vector of the 1st iteration acquisition, wherein

Be f ⁽¹⁾K element,

During for k=1 Value,

During for k=3721 Value, k=1,2 ..., 3 ', () ^TBe matrix transpose.Order

Wherein

Be the linear measurement matrix that the 0th iteration obtains, W ⁽¹⁾Be the weighting matrix that the 1st time iteration obtains,

Be the echo data vector that obtains in the step 2.4, λ=40 are Lagrangian coefficient, () ^HBe conjugate transpose.Forward step 4.5.1 to.

Step 4.5.1:

Definition Be the 1st the slow constantly phase error of n of iteration, wherein

() ^HBe conjugate transpose,

It is the linear measurement matrix that the 0th iteration obtains

N submatrix,

The echo data vector that obtains for step 2.4 N subvector, slow constantly n=1,2 ..., 128, f ⁽¹⁾Be the solution vector that the 1st time iteration obtains, arctan () is arctan function.Forward step 4.6.1 to.

Step 4.6.1:

Definition

Be the linear measurement matrix of the 1st iteration, wherein For

N submatrix,

It is the linear measurement matrix that the 0th iteration obtains N submatrix,

During for n=1 Value,

During for n=128 Value, slow constantly n=1,2 ..., 128, j is pure imaginary number, () ^TBe matrix transpose,

Be the 1st the slow constantly phase error of n of iteration.Forward step 4.7.1 to.

Step 4.7.1:

Because not satisfying

Less than 3 * 10 ^-3Perhaps the value of the count condition that equals 100 is carried out iteration the 2nd time, forwards step 4.2.2 to, wherein f ⁽⁰⁾Be the solution vector that the 0th time iteration obtains, f ⁽¹⁾Be the solution vector that the 1st time iteration obtains, || || ₂Be the L2 norm.

Step 4.2.2:

Carry out iteration the 2nd time, count=2 comprises step 4.3.2 ~ 4.7.2.Forward step 4.3.2 to.

Step 4.3.2:

Definition $W^{\left(2\right)}=\mathrm{diag}(\frac{1}{{\left(\right|f_1^{\left(1\right)}|+\mathrm{\&beta;})}^2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{\left(\right|f_k^{\left(1\right)}|+\mathrm{\&beta;})}^2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{\left(\right|f_{3721}^{\left(1\right)}|+\mathrm{\&beta;})}^2})$ Be the weighting matrix of the 2nd iteration, wherein

Be the solution vector that the 1st time iteration obtains,

Be f ⁽¹⁾K element,

During for k=1

Value,

During for k=3721

Value, k=1,2 ..., 37, β=10 ^-2Be L1 norm Constant of Approximation, () ^TBe matrix transpose.Forward step 4.4.2 to.

Step 4.4.2:

Definition

Be the solution vector of the 2nd iteration acquisition, wherein

Be f ⁽²⁾K element,

During for k=1

Value,

During for k=3721 Value, k=1,2 ..., 37, () ^TBe matrix transpose.Order

Wherein

Be the linear measurement matrix that the 1st iteration obtains, W ⁽²⁾Be the weighting matrix that the 2nd time iteration obtains,

Be the echo data vector that obtains in the step 2.4, λ=40 are Lagrangian coefficient, () ^HBe conjugate transpose.Forward step 4.5.2 to.

Step 4.5.2:

Definition

Be the 2nd the slow constantly phase error of n of iteration, wherein

() ^HBe conjugate transpose, It is the linear measurement matrix that the 1st iteration obtains

N submatrix,

The echo data vector that obtains for step 2.4

N subvector, slow constantly n=1,2 ..., 128, f ⁽²⁾Be the solution vector that the 2nd time iteration obtains, arctan () is arctan function.Forward step 4.6.2 to.

Step 4.6.2:

Definition

Be the linear measurement matrix of the 2nd iteration, wherein

For

N submatrix,

It is the linear measurement matrix that the 1st iteration obtains

N submatrix,

During for n=1

Value,

During for n=128

Value, slow constantly n=1,2 ..., 128, j is pure imaginary number, () ^TBe matrix transpose,

Be the 2nd the slow constantly phase error of n of iteration.Forward step 4.7.2 to.

Step 4.7.2:

Because not satisfying

Less than 3 * 10 ^-3Perhaps the value of the count condition that equals 100 is carried out iteration the 3rd time, forwards step 4.2.3 to, wherein f ⁽¹⁾Be the solution vector that the 1st time iteration obtains, f ⁽²⁾Be the solution vector that the 2nd time iteration obtains, || || ₂Be the L2 norm.

Step 4.2.3

By that analogy, carry out the 3rd iteration ...,

Step 4.3:

This emulation experiment cc=17 is according to the solution vector f that the 17th time iteration obtains ⁽¹⁷⁾, obtain the observation scene scattering coefficient vector α=f that constructs in the step 2.1 ⁽¹⁷⁾By observation scene scattering coefficient vector α=[α ₁..., α _i..., α ₆₁] ^T, α _i=[α _{I, 1}..., α _{I, l}..., α _{I, 61}], i=1,2 ..., 61, l=1,2 ..., 61, obtain the final imaging results of synthetic-aperture radar two-dimensional scene

A wherein _i=[α _{I, 1}..., α _{I, l}..., α _{I, 61}], () ^TBe matrix transpose, i=1,2 ..., 61, l=1,2 ..., 61.

Through above-mentioned steps, obtain the positive side-looking band pattern diameter radar image based on the sparse auto-focus method of weighting.

Emulation and test by the specific embodiment of the invention, the sparse own focus method synthetic aperture radar image-forming method of weighting proposed by the invention, the focusing effect of the diameter radar image that obtains than existing auto-focus method in the situation of sparse scene is better, and secondary lobe is lower.This is that the cost function that the present invention adopts has the constraint of weighting L1 norm and L1 norm close approximation more accurately because the present invention from the angle of optimization problem, has adopted a kind ofly than the more excellent cost function of sparse driving autofocus algorithm.

Claims (1)

1. the sparse driving self-focusing of weighting synthetic aperture radar image-forming method is characterized in that it comprises following step:

The parameter of step 1, the positive side-looking band pattern of initialization polarization sensitive synthetic aperture radar system parameter and the sparse driving auto-focus method of weighting:

Be initialized to as systematic parameter and comprise: the light velocity, note is C; The platform speed vector, note is done Platform initial position vector, note is done

The platform initial position is to the bee-line of observation band, and note is R ₀The electromagnetic wave number of radar emission, note is K ₀The signal bandwidth of radar emission baseband signal, note is B; The radar emission signal pulse width, note is T _PThe radar received beam continues width, and note is T _oThe sample frequency of Radar Receiver System, note is f _sThe pulse repetition rate of radar system, note is PRF; Radar Receiver System receives the ripple door with respect to the delay of the transmitted wave door that transmits, and note is T _DThe length of synthetic aperture of radar, note is L _SarThe observation scope of two-dimensional observation scene distance dimension, note is [r _Min, r _Max], r wherein _MinBe the lower limit of two-dimensional observation scene distance dimension observation scope, r _MaxThe upper limit for two-dimensional observation scene distance dimension observation scope; The observation scope of two-dimensional observation scene azimuth dimension, note is [a _Min, a _Max], a wherein _MinBe the lower limit of two-dimensional observation scene azimuth dimension observation scope, a _MaxThe upper limit for two-dimensional observation scene azimuth dimension observation scope; Synthetic-aperture radar is apart from dimension resolution, and note is Δ r; Synthetic-aperture radar azimuth dimension resolution, note is Δ x; The azimuth dimension sampling number, note is N ₁Distance dimension sampling number, note is N ₂Above-mentioned parameter is the canonical parameter of positive side-looking band pattern polarization sensitive synthetic aperture radar system, and wherein, the platform initial position is to the distance R of scene reference point _c, the electromagnetic wave number K of radar emission ₀, the signal bandwidth B of radar emission baseband signal, radar emission signal pulse width T _P, the radar received beam continues width T _o, the sample frequency f of Radar Receiver System _s, the pulse repetition rate PRF of radar system, Radar Receiver System receive the ripple door with respect to the delay T of the transmitted wave door that transmits _D, the length of synthetic aperture L of radar _Sar, synthetic-aperture radar is apart from dimension resolution ax/r, synthetic-aperture radar azimuth dimension resolution ax/x, azimuth dimension sampling number N ₁Distance dimension sampling number N ₂, in positive side-looking band pattern synthetic-aperture radar design process, determine; Wherein, platform speed vector

Platform initial position vector

Observation scope [a of two-dimensional observation scene azimuth dimension _Min, a _Max] and the observation scope [r of two-dimensional observation scene distance dimension _Min, r _Max] in positive side-looking band pattern synthetic-aperture radar observation program design, determine; According to existing positive side-looking band pattern polarization sensitive synthetic aperture radar system and positive side-looking band pattern synthetic-aperture radar observation program, positive side-looking band pattern synthetic aperture radar image-forming method needs be initialized to be as systematic parameter known; The sparse driving auto-focus method of initialization weighting parameter comprises: Lagrangian coefficient, and note is λ; L1 norm Constant of Approximation, note is β; The sparse driving auto-focus method of weighting is found the solution error threshold, and note is ε; Maximum iteration time, note is MC; Above-mentioned parameter is the required parameter of the sparse driving auto-focus method of weighting, wherein, Lagrangian coefficient lambda, L1 norm Constant of Approximation β, the sparse driving auto-focus method of weighting is found the solution error threshold ε, maximum iteration time MC, being in advance provides;

Step 2, structure radar echo signal and the Systems with Linear Observation model of observing the scene scattering coefficient

May further comprise the steps:

Step 2.1:

Observation scope [r with two-dimensional observation scene distance dimension _Min, r _Max] be divided into N distance dimension unit so that distance dimension resolution ax/r is equally spaced as the interval, note do distance dimension unit 1, distance tie up unit 2 ..., distance dimension unit N, wherein N is positive integer; In like manner, with the observation scope [a of two-dimensional observation scene azimuth dimension _Min, a _Max] uniformly-spaced being divided into M azimuth dimension unit as the interval take azimuth dimension resolution ax/x, note is done azimuth dimension unit 1, and the position vector note of azimuth dimension unit 1 is done

Azimuth dimension unit 2, the position vector note of azimuth dimension unit 2 is done

, azimuth dimension unit M, the position vector of azimuth dimension unit M note is done

Wherein M is positive integer; Through after the above-mentioned processing, the two-dimensional observation scene is divided into K cell, observation scene cell number K=NM, comprise M azimuth dimension unit and N distance dimension unit in K the cell, i azimuth dimension unit in M azimuth dimension unit and N distance are tieed up in the unit l and are remembered apart from the position vector of tieing up the determined cell in unit and do

I=1,2 ..., M, l=1,2 ..., N; The scattering coefficient of two-dimensional observation scene is expressed as vectorial α=[α ₁..., α _i..., α _M] ^T, α wherein _iBe i the subvector of α, α _i=[α _{I, 1}..., α _{I, l}..., α _{I, N}] be the scattering coefficient vector of azimuth dimension unit i, α ₁α during for i=1 _iValue, α _Mα during for i=M _iValue, α _{I, l}Be α _iL element, α _{I, l}The expression cell Electromagnetic scattering coefficient, α _{I, 1}α during for l=1 _{I, l}Value, α _{I, N}α during for l=N _{I, l}Value, i=1,2 ..., M, l=1,2 ..., N, () ^TBe matrix transpose;

Step 2.2:

Synthetic-aperture radar echo data vector note is done

Wherein () ^TBe matrix transpose,

Be the echo data vector that slow constantly n receives, y ₁Y during for n=1 _nValue, Be n=N ₁The time y _nValue, y _{N, m}For synthetic-aperture radar at slow constantly n, the echo data that fast constantly m receives, y _{N, 1}Y during for m=1 _{N, m}Value,

Be m=N ₂The time y _{N, m}Value, slow constantly n=1,2 ..., N ₁, fast constantly m=1,2 ..., N ₂, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number;

Step 2.3:

Structure linear measurement matrix is

Wherein () ^TBe matrix transpose,

Be n the submatrix of Φ,

During for n=1

Value,

Be n=N ₁The time Value, slow constantly n=1,2 ..., N ₁, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number, φ _{N, m}For

M subvector, φ _{N, m}=[γ _{N, m}(1,1), γ _{N, m}(1,2) ..., γ _{N, m}(i, l) ..., γ _{N, m}(M, N-1), γ _{N, m}(M, N)] ^T, φ _{N, 1}φ during for m=1 _{N, m}Value,

Be m=N ₂The time φ _{N, m}Value, fast constantly m=1,2 ..., N ₂, N ₂Be distance dimension sampling number, ${\mathrm{\&gamma;}}_{n,m}(i,l)=\mathrm{rect}\left(\frac{2{\left|\right|{\stackrel{\&OverBar;}{x}}_i-{\stackrel{\&OverBar;}{P}}_n\left|\right|}_2}{L_{\mathrm{sar}}}\right)\&CenterDot;\mathrm{rect}\left(\frac{t_f\left(m\right)-\mathrm{\&tau;}}{T_p}\right)\&CenterDot;\exp \left(\mathrm{j\&pi;}{K}_r{(t_f\left(m\right)-\mathrm{\&pi;})}^2\right),$ γ _{N, m}γ when (1,1) is i=1 and l=1 _{N, m}(i, l) value, γ _{N, m}(1,2 γ when being i=1 and l=2 _{N, m}(i, l) value, γ _{N, m}γ when (M, N-1) is i=M and l=N-1 _{N, m}(i, l) value, γ _{N, m}γ when (M, N) is i=M and l=N _{N, m}(i, l) value, j is pure imaginary number, i=1,2 ..., M, l=1,2 ..., N,

Be the position vector of i azimuth dimension unit of two-dimensional observation scene, L _SarBe the length of synthetic aperture of radar, t _f(m) be the fast constantly time variable of m, chirp rate

B is the signal bandwidth of radar emission baseband signal, T _PBe the radar emission signal pulse width, $\mathrm{\&tau;}=\frac{2R_n(i,l)}{C},$ $R_n(i,l)={\left|\right|{\stackrel{\&OverBar;}{P}}_n-{\stackrel{\&OverBar;}{S}}_{i,l}\left|\right|}_2,$ || || ₂Be the L2 norm, C is the light velocity, the slow constantly position vector of n platform

Be the platform speed vector,

Be platform initial position vector, PRF is the pulse repetition rate of radar system,

For in the two-dimensional observation scene that obtains in the step 2.1 by the position vector of azimuth dimension unit i with the determined cell of distance dimension unit l, slow constantly n=1,2 ..., N ₁, fast constantly m=1,2 ..., N ₂, i=1,2 ..., M, l=1,2 ..., N, M is observation scene azimuth dimension unit number, N is observation scene distance dimension unit number, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number;

Step 2.4:

From 1 to N ₂This N ₂Randomly draw Num in the individual positive integer ₀Individual positive integer and to this Num ₀Individual positive integer obtains the 1st group of positive integer by sorting from small to large, the 1st positive integer note of the 1st group of positive integer done

The 2nd positive integer note of the 1st group of positive integer done

, the Num of the 1st group of positive integer ₀Individual positive integer note is done

In like manner, from 1 to N ₂This N ₂Randomly draw Num in the individual positive integer ₀Individual positive integer and to this Num ₀Individual positive integer obtains the 2nd group of positive integer by sorting from small to large, the 1st positive integer note of the 2nd group of positive integer done

The 2nd positive integer note of the 2nd group of positive integer done , the Num of the 2nd group of positive integer ₀Individual positive integer note is done

, by that analogy, from 1 to N ₂This N ₂Randomly draw Num in the individual positive integer ₀Individual positive integer and to this Num ₀Individual positive integer obtains N by sorting from small to large ₁The group positive integer, N ₁The 1st positive integer note of group positive integer done

N ₁The 2nd positive integer note of group positive integer done

, N ₁The Num of group positive integer ₀Individual positive integer note is done

Num wherein ₀For being less than or equal to N ₂Positive integer, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number; With the echo data vector that obtains in the step 2.2 In the echo data vector that receives of slow constantly n $y_n=[y_{n,1},\&CenterDot;\&CenterDot;\&CenterDot;,y_{n,m},\&CenterDot;\&CenterDot;\&CenterDot;,y_{n,N_2}]$ In

Column element

The

Column element

, the

Column element

Composition of vector

Slow constantly n=1,2 ... ... N _p, obtain thus N ₁Individual vector

During for n=1

Value, Be n=N ₁The time

Value is with the N that obtains ₁Individual vector

Form the echo data vector

Wherein () ^TBe matrix transpose,

For

N subvector, slow constantly n=1,2 ..., N ₁, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number; With the linear measurement matrix that obtains in the step 2.3

In n submatrix

In

Column element

The

Column element

, the

Column element

Form matrix

Slow constantly n=1,2 ..., N ₁, obtain thus N ₁Individual matrix

During for n=1

Value,

Be n=N ₁The time Value is with the N that obtains ₁Individual matrix Form the linear measurement matrix

Wherein () ^TBe matrix transpose,

For

N submatrix, slow constantly n=1,2 ..., N ₁, N ₁Be azimuth dimension sampling number, N ₂Be distance dimension sampling number; The Systems with Linear Observation model of definition observation scene scattering coefficient and radar return data is expressed as Wherein

For with

The Gaussian noise vector that dimension is identical, α is observation scene scattering coefficient vector;

The cost function of step 3, the sparse auto-focus method of structure weighting

The cost function of the sparse auto-focus method of structure weighting is

F=[f wherein ₁..., f _k..., f _K] ^TBe solution vector, f _kBe k element of solution vector, f ₁F during for k=1 _kValue,, f _KF during for k=K _kValue, k=1,2 ..., K, K is the number of observation scene cell, λ is Lagrangian coefficient,

The echo data vector that obtains for step 2.4,

The linear measurement matrix that obtains for step 2.4, || || ₁Be the L1 norm, || || ₂Be L2 norm, () ^TBe matrix transpose, the definition weighting matrix $W_1=\mathrm{diag}(\frac{1}{\left|f_1\right|+\mathrm{\&beta;}},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{\left|f_k\right|+\mathrm{\&beta;}},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{\left|f_K\right|+\mathrm{\&beta;}}),$ The L1 norm approximate value of getting solution vector f is ${\left|\right|f\left|\right|}_1\&ap;\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\left(\right|f_k|-\mathrm{\&beta;}\&CenterDot;\ln (\mathrm{\&beta;}+\left|f_k\right|),$ β is L1 norm Constant of Approximation;

The image-forming step of step 4, the sparse auto-focus method of weighting

May further comprise the steps:

Step 4.1:

The linear measurement matrix that defines the 0th iteration acquisition is ${\mathrm{\&Phi;}}^{\left(0\right)}={[{\mathrm{\&Phi;}}_1^{\left(0\right)},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&Phi;}}_n^{\left(0\right)},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&Phi;}}_{N_1}^{\left(0\right)}]}^T,$ Order

The linear measurement matrix that equals to obtain in the step 2.4

Wherein

Be Φ ⁽⁰⁾N submatrix, During for n=1

Value,

Be n=N ₁The time

Value, slow constantly n=1,2 ..., N ₁, N ₁Be azimuth dimension sampling number, () ^TBe matrix transpose; The solution vector that defines the 0th iteration acquisition is $f^{\left(0\right)}={[f_1^{\left(0\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_k^{\left(0\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_K^{\left(0\right)}]}^T,$ Wherein

Be f ⁽⁰⁾K element,

During for k=1

Value,

During for k=K Value, k=1,2 ..., K, K is the number of observation scene cell, order

Wherein Be the echo data vector that obtains in the step 2.4, () ^HBe conjugate transpose; Definition count is the iterations counting variable, count=1, and 2 ..., MC; Definition cc is iteration number of times of iteration when stopping, and cc is positive integer; Forward step 4.2.1 to, carry out iteration the 1st time;

Step 4.2.1:

Carry out iteration the 1st time, iterations counting variable count=1, the step of the 1st iteration comprises step 4.3.1,4.4.1,4.5.1,4.6.1,4.7.1; Forward step 4.3.1 to;

Step 4.3.1:

Definition $W^{\left(1\right)}=\mathrm{diag}(\frac{1}{{\left(\right|f_1^{\left(0\right)}|+\mathrm{\&beta;})}^2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{\left(\right|f_k^{\left(0\right)}|+\mathrm{\&beta;})}^2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{\left(\right|f_K^{\left(0\right)}|+\mathrm{\&beta;})}^2})$ Be the weighting matrix of the 1st iteration, wherein $f^{\left(0\right)}={[f_1^{\left(0\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_k^{\left(0\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_K^{\left(0\right)}]}^T$ Be the solution vector that the 0th time iteration obtains, Be f ⁽⁰⁾K element, During for k=1 Value,

During for k=K

Value, k=1,2 ..., K, K is the number of observation scene cell, β is L1 norm Constant of Approximation, () ^TBe matrix transpose; Forward step 4.4.1 to;

Step 4.4.1:

Definition $f^{\left(0\right)}={[f_1^{\left(0\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_k^{\left(0\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_K^{\left(0\right)}]}^T$ Be the solution vector of the 1st iteration acquisition, wherein

Be f ⁽¹⁾K element,

During for k=1 Value, During for k=K

Value, k=1,2 ..., K, K is the number of observation scene cell, () ^TBe matrix transpose; Order

Wherein Be the linear measurement matrix that the 0th iteration obtains, W ⁽¹⁾Be the weighting matrix that the 1st time iteration obtains, Be the echo data vector that obtains in the step 2.4, λ is Lagrangian coefficient, () ^HBe conjugate transpose; Forward step 4.5.1 to;

Step 4.5.1:

Definition

Be the 1st the slow constantly phase error of n of iteration, wherein

() H is conjugate transpose,

It is the linear measurement matrix that the 0th iteration obtains

N submatrix,

The echo data vector that obtains for step 2.4

N subvector, slow constantly n=1,2 ..., N ₁, f ⁽¹⁾Be the solution vector that the 1st time iteration obtains, arctan () is arctan function, N ₁Be the azimuth dimension sampling number; Forward step 4.6.1 to;

Step 4.6.1:

Definition

Be the linear measurement matrix of the 1st iteration, wherein

For

N submatrix,

It is the linear measurement matrix that the 0th iteration obtains

N submatrix,

During for n=1

Value, Be n=N ₁The time

Value, slow constantly n=1,2 ..., N ₁, j is pure imaginary number, () ^TBe matrix transpose,

Be the 1st the slow constantly phase error of n of iteration, N ₁Be the azimuth dimension sampling number; Forward step 4.7.1 to;

Step 4.7.1:

If

Value less than ε or count equals maximum iteration time MC, then, makes cc=1, and iteration stops, and forwards step 4.3 to; Otherwise, carry out iteration the 2nd time, forward step 4.2.2 to, wherein cc is iteration number of times of iteration when stopping, ε is error threshold, f ⁽⁰⁾Be the solution vector that the 0th time iteration obtains, f ⁽¹⁾Be the solution vector that the 1st time iteration obtains, MC is maximum iteration time, || || ₂Be the L2 norm;

Step 4.2.2:

Carry out iteration the 2nd time, count=2, the 2nd time iterative step comprises step 4.3.2,4.4.2,4.5.2,4.6.2,4.7.2; Forward step 4.3.2 to;

Step 4.3.2:

Definition $W^{\left(2\right)}=\mathrm{diag}(\frac{1}{{\left(\right|f_1^{\left(0\right)}|+\mathrm{\&beta;})}^2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{\left(\right|f_k^{\left(0\right)}|+\mathrm{\&beta;})}^2},\&CenterDot;\&CenterDot;\&CenterDot;,\frac{1}{{\left(\right|f_K^{\left(0\right)}|+\mathrm{\&beta;})}^2})$ Be the weighting matrix of the 2nd iteration, wherein $f^{\left(1\right)}={[f_1^{\left(1\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_k^{\left(1\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_K^{\left(1\right)}]}^T$ Be the solution vector that the 1st time iteration obtains,

Be f ⁽¹⁾K element,

During for k=1

Value, During for k=K

Value, k=1,2 ..., K, K is the number of observation scene cell, β is L1 norm Constant of Approximation, () ^TBe matrix transpose; Forward step 4.4.2 to;

Step 4.4.2:

Definition $f^{\left(2\right)}={[f_1^{\left(2\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_k^{\left(2\right)},\&CenterDot;\&CenterDot;\&CenterDot;,f_K^{\left(2\right)}]}^T$ Be the solution vector of the 2nd iteration acquisition, wherein

Be f ⁽²⁾K element,

During for k=1

Value,

During for k=K

Value, k=1,2 ..., K, K is the number of observation scene cell, () ^TBe matrix transpose; Order

Wherein

Be the linear measurement matrix that the 1st iteration obtains, W ⁽²⁾Be the weighting matrix that the 2nd time iteration obtains,

Be the echo data vector that obtains in the step 2.4, λ is Lagrangian coefficient, () ^HBe conjugate transpose; Forward step 4.5.2 to;

Step 4.5.2:

Definition

Be the 2nd the slow constantly phase error of n of iteration, wherein

() ^HBe conjugate transpose,

It is the linear measurement matrix that the 1st iteration obtains N submatrix, The echo data vector that obtains for step 2.4

N subvector, slow constantly n=1,2 ..., N ₁, f ⁽²⁾Be the solution vector that the 2nd time iteration obtains, arctan () is arctan function, N ₁Be the azimuth dimension sampling number; Forward step 4.6.2 to;

Step 4.6.2:

Definition

Be the linear measurement matrix of the 2nd iteration, wherein For

N submatrix,

It is the linear measurement matrix that the 1st iteration obtains

N submatrix, During for n=1

Value,

Be n=N ₁The time Value, slow constantly n=1,2 ..., N ₁, j is pure imaginary number, () ^TBe matrix transpose, Be the 2nd the slow constantly phase error of n of iteration, N ₁Be the azimuth dimension sampling number; Forward step 4.7.2 to;

Step 4.7.2:

If

Value less than ε or count equals maximum iteration time MC, then, makes cc=2, and iteration stops, and forwards step 4.3 to; Otherwise, carry out iteration the 3rd time, forward step 4.2.3 to, wherein cc is iteration number of times of iteration when stopping, ε is error threshold, f ⁽¹⁾Be the solution vector that the 1st time iteration obtains, f ⁽²⁾Be the solution vector that the 2nd time iteration obtains, MC is maximum iteration time, || || ₂Be the L2 norm;

Step: 4.2.3

In like manner, by that analogy, carry out the 3rd iteration ..., the MC-1 time iteration;

The MC time iteration of step 4.2.:

Carry out iteration the MC time, count=MC,

This moment, the value of iterations count equaled MC, made cc=MC, and termination of iterations forwards step 4.3 to;

Step 4.3:

The solution vector f that obtains according to the cc time iteration ^(cc), obtain the observation scene scattering coefficient vector α=f that constructs in the step 2.1 ^(cc), cc is iteration number of times of iteration when stopping; By observation scene scattering coefficient vector α=[α ₁..., α _i..., α _M] ^T, i the subvector of α is α i=[α _{I, 1}..., α _{I, l}..., α _{I, N}], α ₁α during for i=1 _iValue, α _Mα during for i=M _iValue, α _{I, l}Be α _iL element, α _{I, 1}α during for l=1 _{I, l}Value, α _{I, N}α during for l=N _{I, l}Value, i=1,2 ..., M, l=1,2 ..., N obtains the final imaging results of synthetic-aperture radar two-dimensional scene $\mathrm{IMG}={[A_1^T,\&CenterDot;\&CenterDot;\&CenterDot;,A_i^T,\&CenterDot;\&CenterDot;\&CenterDot;,A_M^T]}^T,$ A wherein _i=[α _{I, 1}..., α _{I, l}..., α _{I, N}], A ₁A during for i=1 _iValue, A _MA during for i=M _iValue, () ^TBe matrix transpose, i=1,2 ..., M, l=1,2 ..., N, M are the unit number of azimuth dimension, N is the number of distance dimension unit.

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